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Three guys rent a hotel room for $30 which they split for $10.00 each.  The clerk later told them he was running a special and the room was now $25 so he refunded them $5.  They couldn't split the $5 so they each took $1 and gave the clerk $2.  This is a total of $27 plus the $2 for the clerk.  Where is the other $1?

CalifJim · Accepted Answer

navy navy 312the room was now $25 so he refunded them $5.

$25 + $5 = $30

navy navy 312They ... gave the clerk $2 (of the $5)

The clerk now has the $25 (the discounted cost of the room) plus a $2 tip.

$25 + $2 = $27

navy navy 312they each took $1 (of the $5)

There were three of them, so the total they took back was $3.
The clerk now still has $27 and the men have $3.

$27 + $3 = $30 (the original amount)

So what's the problem? There is no extra $1.

navy navy 312This is a total of $27

What is a total of $27? Presumably, the effective cost of the room. Here's how the reasoning goes: Each paid $10 and ended up with $1 back, so in effect each paid $9 for the room.

$9 x 3 = $27

But this is not correct because it doesn't take into account that after paying $9 each, they still had $2 between the three of them to give to the clerk. So saying they each got a discount of $1 is wrong. The discount was greater than that. If you do the calculations, you see that they actually paid only $8.33 each for the room — not $9. Only the fact that they gave away part of their discount ($0.66667) makes it look like their final effective rate was $9 each.

navy navy 312plus the $2 for the clerk.

This $2 belonged to the three men until they decided to give it to the clerk.
So they really haven't paid $9 each. They've paid $2 less (split three ways) but they gave it away. So the $2 is subtracted from $27, not added to it, if you want to know the discounted amount of the room ($25).

$27 - $2 = $25

CJ

By the way, this riddle dates back to the beginning of the universe, if not earlier.

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